Model and parameter selection for optical metrology

ABSTRACT

A profile model for use in optical metrology of structures in a wafer is selected, the profile model having a set of geometric parameters associated with the dimensions of the structure. A set of optimization parameters is selected for the profile model using one or more input diffraction signals and one or more parameter selection criteria. The selected profile model and the set of optimization parameters are tested against one or more termination criteria. The process of selecting a profile model, selecting a set of optimization parameters, and testing the selected profile model and set of optimization parameters is performed until the one or more termination criteria are met.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application relates to co-pending U.S. patent application Ser. No.09/727,530, entitled “System and Method for Real-Time Library Generationof Grating Profiles” by Jakatdar, et al., filed on Nov. 28, 2000; toco-pending U.S. patent application Ser. No. 09/907,488, entitled“Generation of a Library of Periodic Grating Diffraction Signals”, filedJul. 16, 2001, by Niu et al.; to co-pending U.S. patent application Ser.No. 09/737,705 entitled “System and Method for Grating ProfileClassification” by Doddi, et al., filed on Dec. 14, 2000; to co-pendingU.S. patent application Ser. No. 09/770,997, entitled “Caching ofIntra-layer Calculations for Rapid Rigorous Couple-Wave Analyses”, byNiu et al., filed on Jan. 26, 2000; and to co-pending U.S. patentapplication Ser. No. 10/162,516 entitled “Selection of Wavelengths forIntegrated Circuit Optical Metrology, by Doddi, et al., filed on Jun. 3,2002, all owned by the assignee of this application and incorporatedherein by reference.

BACKGROUND OF INVENTION

1. Field of Invention

This application relates to integrated circuit (IC) metrology and moreparticularly to the selection of a structure model and parameters foroptical metrology.

2. Related Art

With the current drive towards smaller geometries of IC devices,measurement of IC device features is increasingly difficult as the sizeof the features become smaller. One method of measuring the featuresinvolves the use of gratings or periodic structures formed in test areasof a wafer that are proximate to or within the devices or circuits onthe wafer. Knowledge of the dimensions of the gratings or periodicstructures is essential in order to determine if the dimensions of thestructure are within acceptable ranges and if, for example, a particularfabrication process causes the sidewalls of the features to be tapered,vertical, T-topped, undercut, or have footings.

Measurement of the periodic structure features may be done with ascanning electron microscope (SEM) or similar device where the sample iscleaved and examined. The cross-section SEM method is typically slow,expensive, destructive, and typically only provides one measurementnumber seen from the top of the feature.

Another measurement technique uses scatterometry. In scatterometry,spectroscopic reflectometry and ellipsometry,multiple-angle-of-incidence (MAI) devices, and mixed design systems aretypically used to shine light on the structure and measure the reflectedlight. Empirical scatterometry basically uses an approach where thediffraction signals are measured for known widths of features of astructure, the pair of diffraction signals and structure widths used tocreate a library. Even for a limited library of structure dimensions andassociated diffraction signals, the empirical scatterometry techniquefor building a library is time consuming and expensive. As theresolution of the structure dimension increases, the size of the libraryincreases while the time to create and use the library increasesconsiderably.

In another measurement technique, instead of using a library ofdiffraction signals and profile data, regression is used to determinethe profile data from the measured diffraction signal. In usingregression, one or more optimization techniques may be used to determinethe profile data from the measured diffraction signal.

The length of time needed to create a library or to make a regressionresult converge varies depending on the profile model used and thenumber of parameters used to represent the profile model in thediffraction signal calculations. Typically, the more complicated theprofile model and the more parameters used, the more time and/orcomputing resources needed to retrieve the desired information frommeasurements.

SUMMARY OF INVENTION

In an exemplary embodiment, a profile model for use in optical metrologyof structures in a wafer is selected, the profile model having a set ofgeometric parameters associated with the dimensions of the structure. Aset of optimization parameters is selected for the profile model usingone or more input diffraction signals and one or more parameterselection criteria. The selected profile model and the set ofoptimization parameters are tested against one or more terminationcriteria. The process of selecting a profile model, selecting a set ofoptimization parameters, and testing the selected profile model and setof optimization parameters is performed until the one or moretermination criteria are met.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is an architectural diagram illustrating the use of opticalmetrology to measure the diffraction signals off wafer periodicstructures.

FIG. 2 is an exemplary flowchart of the overall process for model andparameter selection for optical metrology of integrated circuitstructures.

FIG. 3 is an exemplary flowchart for processing characterization of thewafer structure.

FIG. 4 is an exemplary flowchart for converting characterization of thewafer structure into a model and associated parameters.

FIG. 5 is an exemplary flowchart for selecting parameters of the modelbased on one or more selection criteria.

FIG. 6A is an architectural diagram depicting a system for model andparameter selection in an exemplary embodiment.

FIG. 6B is an architectural diagram of a metrology model optimizer in anexemplary embodiment.

FIG. 6C is an architectural diagram of a metrology model optimizerintegrated with a wafer fabrication cluster.

FIG. 7 is an architectural diagram depicting the use of optimizationengines in an exemplary embodiment.

FIG. 8 is an exemplary architectural diagram of a geometric model of theprofile of a wafer structure.

FIG. 9A is an exemplary geometric shape utilized for building a model ofthe profile of a wafer structure.

FIG. 9B is an exemplary combination of geometric shapes utilized forbuilding a model of the profile of a wafer structure.

FIG. 9C is an exemplary composite structure using a combination ofgeometric shapes as a model of the profile of a wafer structure.

FIG. 10A is an exemplary diagram of a wafer structure model using arectangle and one trapezoid.

FIG. 10B is an exemplary reflectance graph of two highly correlatedparameters of a wafer structure model using a rectangle and onetrapezoid.

FIG. 10C is a table illustrating goodness of fit (GOF) and theconfidence interval of each parameter of the model using a rectangle andone trapezoid.

FIG. 11A is an exemplary diagram of a wafer structure model using arectangle and two trapezoids.

FIG. 11B is an exemplary reflectance graph of two highly correlatedparameters of a wafer structure model using a rectangle and twotrapezoids.

FIG. 11C is a table illustrating the goodness of fit (GOF) andconfidence interval of each parameter of the profile model using arectangle and two trapezoids.

FIG. 12A is an exemplary table of correlation coefficients of parametersof a wafer structure profile model.

FIG. 12B is an exemplary reflectance difference graph of two parametersof a profile model that have complete correlation.

FIGS. 13A to 13D are exemplary profile models using from one to fourtrapezoids to model a wafer structure.

FIG. 13E is an exemplary graph of the cost function and GOF of simulatedsignal versus the measured signal as a function of the number oftrapezoids used in the profile model.

FIG. 14 is an exemplary graph of the cost function and GOF of simulatedsignal versus the measured signal as a function of the number ofparameters used in the profile model.

FIG. 15 is a model and parameter selection data store layout in anexemplary embodiment.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENT(S)

In order to facilitate the description of the present invention, eitheran ellipsometric or reflectometric optical metrology system is used toillustrate certain concepts and principles. Graphs of diffractionsignals off wafer structures using an ellipsometer, e.g., cos (Δ) andtan (Ψ), will be utilized to describe certain exemplary embodimentswhile reflectometric reflectance graphs will be utilized to describeothers. It is understood that the same concepts and principles equallyapply to ellipsometric, reflectometric, or other optical metrologysystems.

FIG. 1 is an architectural diagram illustrating the use of opticalmetrology to measure the diffraction signals off structures patterned ona wafer. The optical metrology system 40 includes a metrology beamsource 41 projecting a beam 43 at the target structure 59 of a wafer 47.The metrology beam 43 is projected at an incidence angle θ_(i) towardsthe target structure 59 and diffracted at a diffraction angle θ_(d) withrespect to normal n. The diffraction beam 49 is measured by a metrologybeam receiver 51. The diffraction beam data 57 is transmitted to aprofile application server 53. The profile application server 53compares the measured diffraction beam data 57 against a library 54 ofcalculated diffraction beam data representing varying combinations ofcritical dimensions of the target structure and resolution of thecritical dimensions. In one exemplary embodiment, the library instancein library 54 best matching the measured diffraction beam data 57 isselected. The profile and associated critical dimensions of the selectedlibrary instance may provide a two-dimensional or three-dimensionalrepresentation of the target structure. The optical metrology system 40may utilize a reflectometer, an ellipsometer, or other optical metrologydevice to measure the diffraction beam or signal. An exemplary opticalmetrology system is described in co-pending U.S. patent application Ser.No. 09/727,530 entitled “System and Method for Real-Time LibraryGeneration of Grating Profiles” by Jakatdar, et al., filed on Nov. 28,2000, and is incorporated in its entirety herein by reference.

FIG. 2 is an exemplary flowchart of the overall process for model andparameter selection for optical metrology of wafer structures. In step310, one or more termination criteria for selection of a structureprofile model are determined. A termination criterion is a yardstickagainst which the result of the selection process is measured. Thetermination criteria may include a cost function value, aGoodness-of-Fit (GOF) value, and/or other curve fitting metrics, as wellas confidence intervals of parameters measured.

For example, a cost function between a simulated signal off thestructure using the profile model parameters compared to a measuredsignal may be used as a termination criterion. One cost functioncomparison is illustrated by the equations below, where V₁ and V₂ aretwo vectors of size n, and the cost function of V₁ relative to V₂ is:

$\begin{matrix}{{{Cost}\left( {V_{1},V_{2}} \right)} = \left( {\sum\limits_{i = 1}^{n}\;\left( {V_{1i} - V_{2i}} \right)^{p}} \right)^{1/p}} & (1.00)\end{matrix}$where i represents the i th member of the vector and p is an arbitrarynumber associated with the metric. The first vector is the set of signalvalues at measurement points for the metrology device used and thesecond vector is the corresponding set of simulated signal values at thesame points. A cost function termination criterion may be set at aspecific number, for example, 0.25. Another termination criterion may bethe goodness of fit (GOF) between the graph of the measured andsimulated signal values. The GOF is a measure of the proximity of twosets of values. For example, when ellipsometric measurements are used,GOF is based on values for tan ψ and cos Δ, where tan ψ and cos Δ arerepresented by a single vector of n dimensions:S=[tan ψ₁ tan ψ₂ . . . tan ψ_(n/2) cos Δ₁ cos Δ₂ . . . cosΔ_(n)]  (1.10)

One commonly used formula for GOF between a measured signal S_(m)compared to a simulated signal S_(s) is:

$\begin{matrix}{{GOF} = {1 - \frac{\sum\limits_{i}^{n}\;\left( {{S_{s}(i)} - {S_{m}(i)}} \right)^{2}}{\sum\limits_{i}^{n}\;\left( {{S_{m}(i)} - {\overset{\_}{S}}_{m}} \right)^{2}}}} & (2.00) \\{{{where}\mspace{20mu}{\overset{\_}{S}}_{m}} = \frac{\sum\limits_{i}^{n}\;{S_{m}(i)}}{n}} & (2.10)\end{matrix}$where i represents the i th measurement point for an optical metrologydevice, n is the total number of measurements for the optical metrologydevice.

Another termination criterion is a confidence interval cutoff value foroptimization parameters. Optimization parameters and confidenceintervals are explained in more detail below. Associated with a profilemodel is a set of geometric parameters. Optimization parameters arederived from the geometric parameters of the profile model. The processof deriving the optimization parameters from the geometric parameterswill also be discussed in detail in FIG. 4. Confidence interval is arange of values of the optimization parameter within which the actualvalue is expected to fall with a specified probability. As anillustration, a 3-sigma confidence interval of an optimization parameterx1 of 20 nm means there is a 99.7% probability that the actual value ofx1 is within+ or −20 nm. The confidence interval amount may be set tothe amount of change from the nominal value of an optimization parameterwhere the change in the diffraction signals is greater than a presetvalue. The preset value may be a value for system noise level orartificial noise level, typically expressed in nanometers. For example,a confidence interval cutoff of 2.0 nm for the middle CD of a structureand 2.5 nm for the bottom CD parameter may be specified. The selectionof the profile model would continue until the confidence interval cutofffor both the middle and bottom CD's are met.

In step 320, one or more criteria for selection of profile modelparameters are determined. Profile selection criteria may include aspecific correlation coefficient or sensitivity of a profile parameter.For example, a cutoff of 0.99 correlation may be used to selectparameters. Alternatively, a specific change in the signal (ΔS) may berequired for each incremental change of the profile parameter (ΔP),where ΔS/ΔP is a measure of the sensitivity of the parameter. Theparameter selection criteria will be discussed in more detail in FIG. 5.

Still referring to FIG. 2, in step 330, the characterization of thewafer structure is obtained. An image of the structure from areferencing metrology instrument, such as a cross section-SEM or X-SEMimage may be used as a basis for characterizing the profile of thestructure. For example, indication of top-rounding, undercutting,T-topping, footing, notching, concavity, convexity, and similarcharacterization of the structure may be obtained. Wafer fabricationprocess design data may be used. Information about the nominal CD andheight together with structure image data may be used to characterizethe structure profile. For a description of the steps involved in oneexemplary process of obtaining characterization of the wafer structure,refer to the description of FIG. 3.

In step 340, the structure characterization is converted into a profilemodel. A profile model may be a simple rectangle with two parametersdesignating the height and width of the rectangle. In FIG. 9A, arectangular shape 920 is shown with two parameters, a0 and a1representing the width and height respectively. Another model for aprofile may be a trapezoid, having three parameters representing forinstance the bottom CD, the top CD, and the height. FIG. 9B represents amodel with two trapezoids 925, one on top of the other. Thetwo-trapezoid profile model 925 could be described using fiveparameters, a0 representing the top CD of the top trapezoid, a1representing the common CD of the top and bottom trapezoids, a2representing the bottom CD of the bottom trapezoid, a3 representing thetotal thickness of the top and bottom trapezoids, and a4 representingthe thickness of the top trapezoid. A more complex profile model isshown in FIG. 9C with two rectangular blocks, 942 and 944, representingtwo different films; a trapezoid 940 that represents the bottom of thepatterned structure having a footing, two rectangular blocks, 938 and936, made of a different material, a thin rectangular block 934representing a notch in the structure, and top trapezoid 932representing some level of rounding in the top of the structure.

As can be seen in FIG. 9C, a profile model may comprise many differentgeometric shapes in order to get a good approximation of the actualprofile of the structure. In general, the more complex the model, themore parameters needed to represent the model. More parameters increasethe complexity and length of time to perform the optical metrologysimulation of the structure. For a description of simulation ofdiffraction signals off a hypothetical structure, refer to co-pendingU.S. patent application Ser. No. 09/770,997, entitled “Caching ofIntra-layer Calculations for Rapid Rigorous Couple-Wave Analyses”, byNiu et al., filed on Jan. 26, 2000, incorporated in its entirety hereinby reference. As will be described in FIG. 5, for a given profile model,the number of parameters may be optimized in order to select the leastnumber of parameters that still meet the termination criteria.

In step 350 of FIG. 2, the profile model optimization parameters areselected based on one or more selection criteria. As will be discussedin more detail in FIG. 5, the selection of an optimization parameter isbased on correlation with other parameters, sensitivity of the simulatedsignal to a change of the optimization parameter, confidence interval ofparameter change that can be detected, and other considerations. Statedanother way, and as an example of an exclusion rule, an optimizationparameter A may be excluded if parameter A is highly correlated toanother parameter B and the simulated signal is insensitive to changesin parameter A.

In step 360, the simulation calculation is optimized by balancing thespeed of simulation computations with the accuracy of the computedsignal. For example, variables such as number or range of diffractionwavelengths used and the number of diffraction orders considered areoptimized to yield the least number of simulation variables and thehighest accuracy of the computed signal.

In step 370, a test is performed to see if the termination criteria aremet. For example, if one of the termination criteria is a cost functionvalue of less than or equal to 2.50, then the cost function value of asimulated signal using the selected parameters of the selected model iscompared to a corresponding measured signal. If the cost function valueis 2.20, then this criterion is met. Additionally, a second terminationcriterion may be a GOF of 0.9990 or greater. Referring to FIG. 11B, thegraph 982 of reflectance on the Y-axis as a function of wavelength onthe X-axis, measured reflectance curve 984 is compared to simulatedreflectance curve 986, the simulation using a double trapezoid profileas illustrated in FIG. 11A. Using the GOF formula, the calculated GOF is0.9994 as shown in FIG. 11C. However, in the same table 988 in FIG. 11C,the highest 3-sigma confidence interval for optimization parameters is17.92 nm for x1. As noted above, the confidence interval is a range ofvalues of the optimization parameter within which the actual value isexpected to fall with a specified probability. As an illustration, a3-sigma confidence interval of an optimization parameter x1 of 20 nmmeans there is a 99.7% probability that the actual value of x1 iswithin + or −20 nm.

Referring now to FIG. 10B, the graph 960 of reflectance on the Y-axis asa function of wavelength on the X-axis, measured reflectance curve 962is compared to simulated reflectance curve 964, the simulation using asingle trapezoid profile as illustrated in FIG. 10A. Using the GOFformula, the calculated GOF is 0.9990 as shown in FIG. 10C. Note that intable 965 of FIG. 10C, the highest 3-sigma confidence interval for theoptimization parameters is 1.99 nm for x0. As explained in more detailbelow, the lower 3-sigma confidence interval of the single trapezoidmodel of FIG. 10A compared to the two trapezoid model of FIG. 11A meansthat the single trapezoid model of FIG. 10A will be selected, given thatthe GOF criterion of 0.9990 is also met.

Referring now to FIG. 2, when the termination criteria are not met,processing proceeds to step 375, where the parameter selection criteriaand/or the profile model is adjusted, and steps 350, 360, and 370 areiterated. Examples of changes to parameter selection criteria may be anadjustment of the correlation cutoff for selecting or excluding aparameter. Alternatively, a sensitivity cutoff, expressed assum-squared-error values as an example, may be adjusted. An example of aprofile model adjustment is using three trapezoids instead of twotrapezoids to represent the structure profile or using one trapezoidinstead of two trapezoids to model the patterned area of the structure.In one instance, the profile model may be revised to include more ordifferent geometric shapes to get closer to the optical microscopy imageof the structure. In another instance, the profile model may be madesimpler, such as using only one trapezoid instead of several trapezoids.

In step 380, when the termination criteria are met, the profile model,the selected profile parameters, the parameter selection criteria, thetermination criteria, and identification data regarding the fabrication,wafer site, and metrology device are saved in a data store.

The results of model and parameter selection may be utilized in severalways. In step 390, a library of simulated diffraction signals andassociated profile data is created using the ranges and resolutions ofthe selected parameters of the selected model. For a description of theprocess for creating a library using ranges and resolutions ofparameters, refer to co-pending U.S. patent application Ser. No.09/727,530 entitled “System and Method for Real-Time Library Generationof Grating Profiles” by Jakatdar, et al., filed on Nov. 28, 2000, and isincorporated in its entirety herein by reference. Alternatively, in step395, the results of model and parameter selections are displayed. In oneembodiment, the values of the critical dimensions, profile shape, andfilm thickness are made available as soon as the one or more terminationcriteria are met. In another embodiment, some or all of the data savedin step 390 are displayed. In still another embodiment, in step 398, theresults of profile model and parameter selection are utilized forfabrication cluster feed-forward or feed-backward control loops. Detailsof this aspect are discussed in FIG. 6C.

As noted above, the description of FIG. 3 provides more detail regardingthe overall flowchart step of obtaining and processing characterizationof the wafer structure. It is understood that the process described inthe following steps is but one technique of obtaining thecharacterization of the wafer structure. Other techniques may includestructure characterization obtained from an integrated circuitfabrication process or from integrated circuit device simulationsoftware.

Referring to FIG. 3, in step 410, one or more data gathering criteria isset. A data-gathering criterion is used to test whether sufficient dataabout the structure is available to perform the model and parameterselection. Examples of data gathering criterion may be a cost functionvalue or GOF similar to the termination criteria used in model andparameter selection. However, the cost function value or GOF may bedifferent, typically lower, from those specified for the terminationcriteria. Other data gathering criteria may include a range ofacceptable variation of measured diffraction signals, such as 3-sigmawidth of measured diffraction signals for the same site in the wafer.For example, if the measured diffraction signals for the same site in awafer have large standard deviation, then additional diffraction signalsmeasurements of the wafer structure may be needed. Alternatively, thedata gathering criteria may be a comparison of the structure profilederived from simulations to an X-SEM image.

Still referring to FIG. 3, in step 420, characterization about the layerstack, unpatterned layer thickness, index of refraction index n,extinction coefficient k, and other layer properties are obtained.Characterization includes the type of material used in each layer. Instep 430, the pitch of the patterned structure, line-to-space ratio,optical characteristics of the patterned structure, and othercharacterization of the patterned structure profile are obtained. Othercharacterization of the patterned structure profile includes data abouttop rounding, undercut, footing, notching, or other expected anomaliesin the profile.

In step 440, measured optical metrology diffraction signals are selectedfrom the input measured diffraction signals. The type and amount of datavaries according to whether an ellipsometer, reflectometer, or otherscatterometric device is used, and depending on the manufacturer of thedevice. Selection of measured diffraction signals involves several stepsdesigned to test a small number of representative diffraction signalsusing selection techniques such as clustering, correlation, and thelike. The measured diffraction signals are categorized into groups usingone or more of the selection techniques listed above. For a descriptionof clustering in optical metrology, refer to co-pending U.S. patentapplication Ser. No. 09/737,705 entitled “System and Method for GratingProfile Classification” by Doddi, et al., filed on Dec. 14, 2000,incorporated in its entirety herein by reference. Representatives ofeach cluster or group of highly correlated measured diffraction signalare identified and selected for use in the model and parameter selectionprocessing.

In step 450, the signal off a structure is simulated utilizing the layerstack and structure profile developed from the characterization of theprofile. For a description of simulation of diffraction signals off ahypothetical structure, refer to co-pending U.S. patent application Ser.No. 09/770,997, entitled “Caching of Intra-layer Calculations for RapidRigorous Couple-Wave Analyses”, by Niu et al., filed on Jan. 26, 2000,incorporated in its entirety herein by reference.

In step 460 of FIG. 3, a test is performed to see if the one or moredata gathering criteria are met. For example, if the GOF between thesimulated signal and the measured diffraction is 0.950 and a datagathering criterion is a GOF of 0.950 or lower, then the data gatheringcriterion is met. In another example, the data-gathering criterion is asimulated thickness of each layer of the stack being the same or withina given percent of the characterization data provided by the user.Assume the thickness of layer of the stack is given as 100 nm and thesimulated thickness for that layer is 102 nm, and assuming one datagathering criterion is a variance of 2 percent or less on layerthickness, then the data gathering criterion is met.

Still referring to FIG. 3, in step 480, the data gathering criteria,wafer and structure characterization, and metrology deviceidentification data are saved. If the data gathering criteria are notmet, in step 470, additional characterization data is obtained or thedata gathering criteria are adjusted. For example, if a data-gatheringcriterion is a cost function value of the simulated signal and measuredsignal of 3.50 or better, and the computed cost function value is 7.00,then the data gathering criterion is not met. A basic characterizationdata may be off. For example, if the pitch of the structure is specifiedincorrectly or the profile characterization is grossly incorrect, thecost function value could be very high. A review of the characterizationdata and accuracy of input of these characterizations into the systemmay be used to identify the cause of the problem. Alternatively, thedata gathering criteria may be adjusted if found to be set incorrectly.

As noted above, the description of FIG. 4 that follows provides moredetail regarding the overall flowchart step of convertingcharacterization of the wafer structure into a model and associatedparameters. In step 510, the types of geometric shapes for each materialof the stack are determined. For example, where there is only onematerial in a stack, one geometric shape may be chosen to represent theentire profile model. In FIG. 8, assuming structure 900 is formed of onematerial, a set of rectangular shapes of varying dimensions (e.g.,rectangular shapes 902, 904, 906, 908, and 910) is used to represent theprofile model of structure 900. In FIG. 9A, for an unpatterned film, arectangular shape is used, whereas in FIG. 9B, two trapezoidal shapesare used. The profile in FIG. 9C utilizes rectangular and trapezoidalshapes.

With reference to FIG. 4, in step 520, the geometric shapes andparameters of the stack of the structure are generated. For example, ifthe first layer in an unpatterned stack is represented by therectangular shape 920 in FIG. 9A, then the geometric parameter is thethickness of the first layer, a1, since the width for an unpatternedlayer can be assumed to be infinite for diffraction simulation purposes.

If the geometric shape for a layer is a trapezoid, three geometricparameters can be used, namely, the top width, the bottom width, andheight of the trapezoid. If a double-trapezoid 925 is used as in FIG.9B, then five geometric parameters can be used, namely, the top width ofthe top trapezoid a0, the bottom width of the top trapezoid a1, which isalso the top width of the bottom trapezoid, the bottom width of thebottom trapezoid a2, the total thickness of the structure model a3, andthe thickness of the top trapezoid a4.

The profile model 930 of FIG. 9C depicts a complex profile model wherethe model includes rectangular shapes 936, 938, 942, and 944, arectangular shape to illustrate notching in the structure 934, andtrapezoidal shapes 932 and 940 to illustrate a top rounding of thestructure and a bottom footing of the structure respectively. Thegeometric parameters are the sum of individual geometric parameters ofthe individual geometric shapes. For the complex profile model 930 ofFIG. 9C, the number of geometric parameters is high. Typically, the moregeometric shapes, the higher the number of geometric parameters.Furthermore, the higher number of geometric parameters of a profilemodel results in a longer simulation process for determining thesimulated diffraction signals. As mentioned previously, a longerdiffraction simulation process may result in a considerably longerlibrary creation time or regression time.

In step 530 of FIG. 4, the nominal values and ranges of the geometricparameters are obtained. These values and ranges are typically obtainedfrom historical or test data for the fabrication process or recipe. Forexample, a top width or top CD may have a nominal value of 200 nm and arange of 120 to 280 nm.

In step 540, the dependencies of the geometric parameters are defined.Again, the dependencies of the geometric parameters are based onhistorical or test results for the particular fabrication process ofrecipe. For example, in a shallow trench isolation (STI) structurehaving a silicon nitride cap and a silicon trench, the nitride captypically determines the CD of the top width of the silicon trench. Inthis case, the independent geometric parameter is the nitride cap bottomCD. The top CD of the nitride cap and the top width of the silicontrench may be tied to the bottom CD of the nitride cap.

Using the double-trapezoid model 925 of FIG. 9B as an example, the topwidth a0 of the top trapezoid may be a function of the bottom width a1of the top trapezoid; a0 may have a linear relation to a1; for example,a0 may be equal to a1 plus a constant or a0 may be equal to a1multiplied by a fixed number. The relation of a geometric parameter toanother geometric parameter may be characterized by a simple linearfunction, a quadratic function, polynomial function or the like.Dependencies of the geometric parameters of the profile model aredefined based on whether a geometric parameter is an independentparameter, has a fixed offset from other parameters, has a variableoffset from other parameters, or has a fixed value. For the sake ofillustration, consider the double trapezoid of FIG. 9B having fivegeometric parameters. From design or previous experience with thefabrication recipe, a0 may be known as an independent parameter. Alsofrom previous fabrication data, a1 may be known to have an constantoffset from a0 of 10 nm, a2 has a variable offset from a0, a3 is aconstant, and a4 is two times a0.

Still referring to FIG. 4, in step 550, the geometric parameters areconverted to optimization parameters, x. Reasons for conversion ofgeometric parameters into optimization parameters include reduction ofthe search space for regression to determine the optimized simulationdiffraction signal (discussed later in FIG. 5). Another reason forconversion of geometric parameters into optimization parameter isreduction of correlation of a parameter to the other parameters.

The result of the conversion is an equation in terms of the optimizationparameter x₁ For example, the equation for each geometric parametera_(i of) the double trapezoid shown in FIG. 9B, having the dependenciesdescribed above is as follows:a0=x0,a1=x0+10,a2=x0+x1,a3=50a4=2x0,where a0, a1, a2, a3, and a4 are the geometric parameters of the profilemodel as defined above, expressed in nanometers, and x0 and x1 are theoptimization parameters of the profile model. Note that the fivegeometric parameters have been converted into two optimizationparameters. It should be noted that more complicated profile models maytypically require more geometric parameters and may generally require acorresponding higher number of optimization parameters. It is understoodto a person knowledgeable in the art, that other equivalent ways ofexpressing the dependencies of the geometric parameters to optimizationparameters may be used.

As noted above, the description of FIG. 5 that follows provides moredetail regarding the overall flowchart step of selecting parameters ofthe model based on one or more selection criteria. Referring to FIG. 5,in step 810, the optical metrology wavelengths or range of wavelengthsfor profile model selection are selected. For a description of theprocess to select wavelengths, refer to co-pending U.S. patentapplication Ser. No. 10/162,516, entitled “Selection of Wavelengths forIntegrated Circuit Optical Metrology”, by Doddi, et al., filed on Jun.3, 2002, incorporated herein in its entirety by reference. Several tasksmay be concurrently or serially performed to provide information as towhether an optimization parameter should be selected or excluded.

In step 820, the correlation between the optimization parameters isdetermined. Typically, a correlation coefficient, r, between twooptimization parameters is calculated using the formula:

$\begin{matrix}{r = \frac{\sum\limits_{i}^{\;}\;{\left( {x_{i} - \overset{\_}{x}} \right)\left( {y_{i} - \overset{\_}{y}} \right)}}{\sqrt{\sum\limits_{i}^{\;}\;\left( {x_{i} - \overset{\_}{x}} \right)^{2}}\sqrt{\sum\limits_{i}^{\;}\;\left( {y_{i} - \overset{\_}{y}} \right)^{2}}}} & (2.60)\end{matrix}$where x₁ and y₁ is a pair of optimization parameters, x is the mean ofx_(i)'s and y is the mean of y_(i)'s. The value of r lies between −1 and+1 inclusive. A correlation coefficient value of +1 can correspond tocomplete positive correlation and a value of −1 can correspond tocomplete negative correlation. A value of r close to zero can correspondto the x and y optimization parameters not being correlated.

Referring to FIG. 12A, the table of correlation coefficients 996 showsfive optimization parameters, namely, x0 representing the resist top CD,x1 representing the resist bottom CD, x2 representing the resistthickness, x3 representing the anti-reflective coating thickness, and x4representing the silicon dioxide thickness. The correlation coefficienttable 996 is configured such that the Y-axis and the X-axis have theparameter numbers shown. An intersection or cell represents thecorrelation coefficient of a parameter matched to a different parameter.For example, at the intersection of parameter x0 and x4, cell 997, thecorrelation coefficient is 0.47. The correlation coefficient iscalculated by substituting input measured values of x0 for x, and x4 fory, in equation 2.60 above. The low correlation coefficient value meansthat parameter x0 and x4 are not highly correlated. In contrast, at theintersection of parameter x3 and x4, cell 998, the correlationcoefficient is 1.00, meaning complete positive correlation between x3and x4. As can be seen in FIG. 12B, the reflectance difference graphversus wavelength of parameter x3, graph 992, has complete positivecorrelation to the reflectance difference graph versus wavelength ofparameter x4, graph 994. In terms of optimization parameter selection,only one of parameter x3 and x4 need to be included, since the variationof the diffraction signals caused by either x3 or x4 can be determinedfrom the variation of the other.

In step 830 of FIG. 5, the confidence interval of each optimizationparameter is determined. As previously noted, the confidence intervalmay be set to the amount of change from the nominal value of anoptimization parameter where the change in the diffraction signals isgreater than the noise level. The noise in the diffraction signals maybe due to system noise, for example, noise from the measurement devices,or the noise may be simulated. The confidence interval is generallyexpressed as a multiple of the standard deviation sigma, σ, of theoptimization parameter. The standard deviation for an optimizationparameter is calculated from measured values of the optimizationparameter, using the formula:

$\begin{matrix}{\sigma = \sqrt{\left( {\left( \left\lbrack {1/\left( {N - 1} \right)} \right\rbrack \right)*\left( {x_{i} - x_{a\; v}} \right)^{2}} \right)}} & (2.70)\end{matrix}$where N is the number of measurements, x_(i) is the i th value of theoptimization parameter x, and x_(av) is the average value of theoptimization parameter x.

The confidence interval is typically calculated from a given set ofsample input data representing actual measurements off the waferstructure. The confidence interval may also be calculated usingsimulated random noise introduced in the measurement data for theoptimization parameter.

With reference to FIG. 10A, the structure profile model 950 using asingle trapezoid 951 on top of a rectangular shape 953 representing astructure with a single layer of underlying film has four optimizationparameters, namely, x0 representing the top CD of the structure, x1representing the bottom CD of the structure, x2 representing the widthof the structure, and x3 representing the width of the underlying film.With reference to FIG. 10C, a table 965 is shown with the 3-sigmaconfidence interval for the four-optimization parameters. For example,optimization parameter x0 has a confidence interval of 1.99 nm, meaningthat measurement of x0 has a probability of 99.7% being visible orsensitive to within 1.99 nm. Alternatively, if the change in x0 is lessthan 1.99 nm, then there is a 99.7% probability the change would notshow in the signal. Similarly, x1 has a 3-sigma confidence interval of1.95 nm, and so on. Note that parameter x3 has a 3-sigma confidenceinterval of 0.30, meaning that parameter x3 is sensitive to changesgreater than 0.30 nm.

Assuming that the same structure as discussed in FIG. 10A was modeledusing two trapezoids 972 on top of a rectangular shape 974 as in theprofile model 970 in FIG. 11A. The double-trapezoid profile model 970has six optimization parameters, namely, x0 representing the top CD ofthe top trapezoid 976, x1 representing the middle CD of the bottomtrapezoid 978, x2 representing the bottom CD of the bottom trapezoid978, x3 representing the width of the double trapezoid 972, x4representing the ratio at the inflection point, equal to h1, the widthof the top trapezoid 976, over the width of the double trapezoid 972,and x5 representing the width of the underlying film. With reference toFIG. 11C, a table 988 is shown with the 3-sigma confidence interval forthe six-optimization parameters. For example, optimization parameter x0has a confidence interval of 6.81 nm, meaning that measurement of x0 hasa probability of 99.7% being visible or sensitive to within 6.81 nm.Alternatively, if the change in x0 is less than 6.81 nm, there is 99.7%probability the change in x0 would not show in the signal. As will bediscussed in a later step 870, the entire collection of data calculatedfor each optimization parameter can be integrated into a decision-makingstep as to whether to include or exclude an optimization parameter.

In step 840 of FIG. 5, the sensitivity of the simulated signal tochanges in one or more optimization parameters is determined. Typically,this determination is done by changing one optimization parameter by asmall amount and keeping the other optimization parameters constant. Forexample, in the profile model in FIG. 10A using one trapezoid, thesensitivity of parameter x0 may be tested by adding one nanometer to thenominal value while keeping x1, x2, and x3 at nominal value andsimulating the signal. If there is no noticeable change in the signalmatrix or graph of (x0 at nominal plus 1 nm), then x0 has lowsensitivity. The other optimization parameters can similarly be changedwhile holding the rest constant in order to test the sensitivity of eachoptimization parameter.

The sensitivity of an optimization parameter may be quantitativelyexpressed by calculating the sum-square-error (SSE) of the changedsignal compared to the signal using nominal values. The SSE formula isas follows:

$\begin{matrix}{{SSE} = {\sum\limits_{i = 1}^{n}\;\left( {{S_{o}(i)} - {S_{1}(i)}} \right)^{2}}} & (3.00)\end{matrix}$where i is the signal simulation point, typically at a presetwavelength, n is the number of signal simulation points, S₀ is thesimulated signal value using nominal values of optimization parameters,S₁ is the simulated signal value using nominal plus change in one of theoptimization parameters.

In step 870 of FIG. 5, the final selection of optimization parameters ismade based on one or more selection criteria. For example, a parameterselection criterion may be a cutoff point in the correlationcoefficient. Parameters with a correlation coefficient lower than 0.50with respect to all other parameters may be selected. Alternatively, apair of parameters with a correlation coefficient of 0.98 may be furthertested as to sensitivity in order to determine which parameter isselected, or which parameter is excluded. An SSE threshold may be usedto select optimization parameters. For example, an SSE threshold of 0.01may be used to filter optimization parameters that are relativelyinsensitive to changes of the parameter. A certain cutoff for the3-sigma confidence interval may also be used to screen out optimizationparameters that do not meet these criteria or to flag profile modelsthat do not yield the proper sensitivity of key parameters critical tothe IC design. A combination of the above criteria may be used. It isunderstood that other equivalent criteria known to one knowledgeable inthe art may be used. If an optimization parameter is not selected, thenthe optimization parameter is set to a fixed value, the fixed valuedetermined from fabrication data or previous experience with the recipe.

In step 890, a procedure is performed to determine the optimizedsimulation diffraction signal to the measured signal using the selectedoptimization parameters of the selected profile model. One embodimentuses a regression technique to get to the optimized simulation signal.One or more types of regression engines may be used.

With reference to FIG. 7, a profile model tester 1400 receives theselected profile model, selected optimization parameters, and measureddiffraction signals 1402. The profile model tester 1400 processes theinput data and activates one or more optimization engines, such asbranch-and-bound technique 1420, simulated annealing 1430, geneticalgorithm 1440, other global optimization technique 1450, or hybridglobal and local optimization technique 1460. The optimization enginesarrive at a global minimum of the difference between the simulatedsignal and the measured signal. The simulated signal corresponding tothe global minimum in turn corresponds to a set of values of theoptimization parameters of the selected profile model, which the profilemodel tester 1400 creates as an output 1404.

FIG. 6A is an architectural diagram depicting a system for model andparameter selection in one exemplary embodiment. In the presentembodiment, a terminal 1800 is used to enter wafer fabrication processdesign data including the characteristic of process and modelingattributes such as the stack, n and k values, nominal profile parametervalues and ranges, width nominal values and ranges, measured diffractedsignals off several sites in the wafer, and structure image data tocharacterize the structure profile. In one example, as described withregard to FIG. 20, the input data may be transmitted to a templateselector and used to select a suitable template based on the particularcharacteristics of process and modeling attributes that are known.Choices of termination and optimization parameter selection criteria mayalso be entered on the terminal 1800 and transmitted as input 1801 to aprofile compiler 1810 and input 1803 to a model generator 1820. Theprofile compiler 1810 edits the input data 1801 and invokes an opticalmetrology simulator 1860 to simulate the signal with the specifiednominal values of the geometric parameters of the profile model 2000.The optical metrology simulator 1860 transmits the simulated diffractionsignal 2001 to the profile compiler 1810. As mentioned above, adescription of simulation of diffraction signals off a hypotheticalstructure, refer to co-pending U.S. patent application Ser. No.09/770,997, entitled “Caching of Intra-layer Calculations for RapidRigorous Couple-Wave Analyses”, by Niu et al., filed on Jan. 25, 2001,incorporated in its entirety herein by reference. The profile compiler1810 performs a comparison of the simulated signal 2001 to the measuredsignal from the input 1801, sending data to terminal 1800 regarding thequality and adequacy of the input data 1801. The profile compiler 1810may also process adjusted profile model data 2012 from a profile modeltester 1840.

Referring to FIG. 6A, the profile compiler 1810 transmits the editedcharacterization data and measured diffraction signals 1811 to a modelgenerator 1820. The model generator 1820 creates a profile model of thestructure comprising geometric shapes. The geometric shapes areexpressed in terms of geometric parameters and converted intooptimization parameters 1821, which are transmitted to a parameterselector 1830. The parameter selector 1830 uses optimization parameterselection criteria to select which optimization parameters meet thecorrelation coefficient cutoff, the sensitivity threshold, and/orconfidence interval requirements from the customer. The parameterselector 1830 invokes the optical metrology simulator 1860 to performsimulations of diffraction signals with profile parameter data 2004. Inturn, the optical metrology simulator 1860 performs simulation of thediffraction signal and transmits simulated diffraction signals 2005 tothe parameter selector 1830.

Part of the parameter selector 1830 function is to perform a procedureto determine the optimized simulated signal for each measured signal,invoking one or more optimization engines discussed in FIG. 7. After theoptimization process, the optimized profile data comprising profile, CD,and film thickness is transmitted as output 2006 to critical dimensionserver 1870. The parameter selector 1830 transmits the selectedoptimization parameters 1831 to the profile model tester 1840, where thetermination criteria such as cost function value, GOF, and/or othertermination criterion are tested. If the termination criteria are notmet, the profile model tester 1840 adjusts the profile model, forexample, by switching from a two-trapezoidal model to a singletrapezoidal model or switching from a simple geometric model to oneusing more geometric shapes to approximate the profile model moreclosely. The adjusted profile model 2012 is transmitted to the profilecompiler 1810. Alternatively, if the termination criteria are met, theprofile model tester 1840 stores the profile model termination criteria,optimization parameter selection criteria, fabrication process, wafersite, optical metrology device identification data, and selectedoptimization parameters 2010 in a data store 1850. The profile modeltester 1840 transmits the optimization parameters 1841 to a librarygenerator 1880, which creates a library 1890 comprising diffractionsignals and associated profile data 1881, using the ranges andresolution of the selected optimization parameters.

FIG. 6B is an architectural diagram depicting a system for model andparameter selection in an exemplary embodiment. Metrology modeloptimizer 1900 receives requests 1902 for critical dimensions, profiles,and film thickness of measured diffraction signals from a profilerworkstation 1910. Based on this request 1902 and other input data (notshown) characterizing the subject structure on the wafer, metrologymodel optimizer 1900 selects a model and parameters in a process similarto that described in FIG. 6A. The metrology model optimizer 1900produces the requested critical dimensions, profiles, and film thicknessassociated with a measured diffraction signals and transmits theseresults 1901 back to the profiler workstation 1910. The profilerworkstation 1910 may be located at a remote user site. Access to themetrology model optimizer 1900 may be through a private network or apublic network like the Internet.

FIG. 6C is an architectural diagram of a metrology model optimizer in anexemplary embodiment. The system configuration is similar to the systemin FIG. 6B except that instead of processing request for criticaldimension data 1924 exclusively from the profiler workstation 1925,in-line requests 1931 for the same data is transmitted from an opticalmetrology system 1930. The optical metrology system 1930 is coupled to afabrication cluster 1940, which may be a clean track unit, lithographymachine, an etch machine or a combined lithography-and-etch unit. As awafer (not shown) completes a fabrication process step, structures onthe wafer are measured by the optical metrology system 1930 creatingmeasured diffraction signals 1931 transmitted to the metrology modeloptimizer 1920. In addition to the critical dimension data 1924 beingtransmitted to the profiler workstation 1925, the same data istransmitted to the fabrication cluster 1940 for advanced process controluse. The critical dimension data 1924 may be used by the fabricationcluster 1940 to adjust process variables of the fabrication process. Theprofiler workstation 1925 sends requests 1926 for critical dimensions,profiles, and film thickness of measured diffraction signals and otherinput data (not shown) characterizing the structures on the wafer orlocation of similar data stored in the metrology model optimizer 1920.The optical metrology system 1930 receives transmitted data 1941 fromthe fabrication cluster 1940 regarding completion of one or morefabrication processes. After completing the measurements of structureson the wafer, the optical metrology system transmits signals 1941 to thefabrication center 1940 to indicate completion of optical metrologymeasurements.

FIGS. 13A, 13B, 13C, and 13D are exemplary structure profiles usingdifferent profile models. FIG. 13A illustrates a structure modeled witha single trapezoid Ti, whereas FIG. 13B illustrates the same structuremodeled with two trapezoids T1 and T2. In similar manner, FIG. 13Cillustrates the same structure modeled with three trapezoids T1, T2, andT3, whereas FIG. 13D illustrates the same structure modeled with fourtrapezoids T1, T2, T3, and T4.

As can be seen in FIGS. 13A and 13B, matching of the structure shape tothe model is not close in FIG. 13A, but FIG. 13B with two trapezoidsshows a dramatic increase in the match between the model and thestructure shape. There are some further but minor improvements in themodels matching the structure shape as the number of trapezoids usedincreases to three and four.

FIG. 13E illustrates exemplary graphs of the cost function and GOF ofsimulated diffraction signals versus the measured signals as a functionof the number of geometric shapes used in the profile model. Graph 1000illustrates how the cost function and GOF varies as the number oftrapezoids used in the profile model is increased. As can be seen in thecost function graph 1004, the cost function value of modeling thestructure depicted in FIG. 13A with one trapezoid is relatively high at3.0. The cost function graph 1004, using the left Y-axis, dropsdramatically to about 1.5 with two trapezoids, less as the number oftrapezoids increases from two to three and from three to fourtrapezoids. The GOF graph 1002, using the right Y-axis, increasesdramatically from a GOF of about 0.920 to 0.97 when the numbertrapezoids increases from one to two, less as the as the number oftrapezoids increases from two to three and from three to fourtrapezoids. As discussed previously, the profile model selectiondetermines the simplest combination of geometric shapes in the profilemodel that meets or exceeds the termination criteria, which may be acost function value and/or a GOF value. As also discussed above, theprofile model may be a combination of different types of geometricshapes, where trapezoid is just one possible shape that can be used.

FIG. 14 is an exemplary graph of the cost function and GOF of simulateddiffraction signals versus the measured signals as a function of thenumber of parameters used in the profile model. Graph 1100 illustrateshow the cost function and GOF varies as the number of parameters used inthe profile model is increased. As can be seen in the cost functiongraph 1104, the cost of modeling a hypothetical structure with threeparameters is relatively high at 2.9. The cost function graph 1104,using the left Y-axis, drops dramatically to about 1.6 with fiveparameters, less as the number of parameters increases from five to sixand from six to seven parameters. The GOF graph 1102, using the rightY-axis, increases dramatically from a GOF of about 0.915 to 0.965 whenthe number of parameters increased from three to five, less as thenumber of parameters increases from five to six and from six to sevenparameters.

As discussed previously, the optimization parameter selection selectsparameters that are uncorrelated, have high sensitivity, and allowsdetection of the change in parameter size required by the application.The selected optimization parameters of the profile model are used tosimulate the diffraction signals for different profile dimensions, andthe simulated diffraction signals are compared to the correspondingmeasured signals to calculate the cost function and GOF. Once theprofile model selected and the selected optimization parameters of theselected profile model provide simulated diffraction signals resultsthat meet or exceed the termination criteria, then the selection processis complete. As discussed above, the regression results such as CD's,film thickness, and profile from the parameter selector 1830 of FIG. 6Amay be used by a system user to fine-tune the recipe or fabricationprocess. Alternatively, the regression results may be used to adjustvariables and/or physical controls of the fabrication process. As alsonoted above, the profile model and optimization parameters selected maybe used to create a library of simulated signals and associated profiledata.

FIG. 15 is a storage layout of data store layout in an exemplaryembodiment. The data store format 1200 for selected model and parametersincludes fabrication process, wafer site, structure, and opticalmetrology device identification data 1210. The data store format 1200may include one or more data segments, each data segment comprising thetermination criteria 1220, selected model identification 1230 andoptimization parameter selection criteria 1240, and selectedoptimization parameters 1, 2, . . . n, 1250. For example, the modelidentification may be Shallow Trench Isolation Single Trapezoid Model,termination criteria may include a cost function of 1.5 and GOF of0.995, optimization parameter selection criteria may be a correlationcoefficient of 0.50 and sensitivity of 0.01 SSE, and the selectedoptimization parameters may be resist top CD, resist bottom CD, resistthickness, anti-reflective coating thickness, and silicon dioxidethickness.

It is contemplated that functional implementation of the exemplaryembodiments described herein may be implemented equivalently inhardware, software, firmware, and/or other available functionalcomponents or building blocks. Other variations and embodiments arepossible in light of above teachings, and it is thus intended that thescope of invention not be limited by this Detailed Description, butrather by claims following.

1. A method of selecting a profile model and selecting parameters of theprofile model for use in optical metrology of structures in a wafer, themethod comprising: a) setting one or more termination criteria; b)setting one or more parameter selection criteria; c) selecting a profilemodel for use in optical metrology of a structure in a wafer, theprofile model having a set of geometric parameters associated withdimensions of the structure; d) selecting a set of optimizationparameters for the profile model using one or more input measureddiffraction signals and the one or more parameter selection criteria,wherein the set of optimization parameters is converted from the set ofgeometric parameters, and wherein the number of optimization parameterswithin the set of optimization parameters is less than the number ofgeometric parameters within the set of geometric parameters; e) testingthe selected profile model and the set of optimization parametersagainst the one or more termination criteria; and f) performing thesteps c, d, and e until the one or more termination criteria are met. 2.The method of claim 1 wherein testing the selected profile model and theset of optimization parameters against the one or more terminationcriteria includes: testing if a simulated diffraction signal costfunction value is less than or equal to a preset cost function value,the simulated diffraction cost function value calculated by comparing anoptimized simulated diffraction signal to a measured diffraction signal.3. The method of claim 1 wherein testing the selected profile model andthe set of optimization parameters against the one or more terminationcriteria includes: testing if a simulated diffraction signal goodness offit value is equal to or greater than a preset goodness of fit value,the simulated diffraction signal goodness of fit value calculated bycomparing an optimized simulated diffraction signal to a measureddiffraction signal.
 4. The method of claim 1 wherein testing theselected profile model and the set of optimization parameters againstthe one or more termination criteria includes: testing if one or morecalculated confidence interval values are less than or equal tocorresponding preset confidence interval values, the confidence intervalbeing a range of values of an optimization parameter within which theactual value is expected to fall with a specified probability.
 5. Themethod of claim 1 wherein testing the selected profile model and the setof optimization parameters against the one or more termination criteriaincludes: testing if a simulated diffraction signal cost function valueis less than or equal to a preset cost function value, the simulateddiffraction cost function value calculated by comparing an optimizedsimulated diffraction signal to a measured diffraction signal; andtesting if the simulated diffraction signal goodness of fit value isequal to or greater than a preset goodness of fit value, the simulateddiffraction signal goodness of fit value calculated by comparing thebest match simulated diffraction signal to the measured diffractionsignal.
 6. The method of claim 5 wherein testing the selected profilemodel and the set of optimization parameters against the one or moretermination criteria flax-that includes: testing if one or morecalculated confidence interval values are less than or equal tocorresponding preset confidence interval values, the confidence intervalbeing a range of values of an optimization parameter within which theactual value is expected to fail with a specified probability.
 7. Themethod of claim 1 wherein the one or more parameter selection criteriacomprise: a correlation cutoff, the correlation cutoff being acorrelation coefficient between an optimization parameter and anotheroptimization parameter of the profile model.
 8. The method of claim 1wherein the one or more parameter selection criteria comprise: asensitivity threshold of an optimization parameter, the sensitivitythreshold being the sum-squared-error of a first simulated diffractionsignal calculated using nominal values for all the optimizationparameters compared to a second simulated diffraction signal calculatedusing an adjusted value of the optimization parameter and nominal valuesfor all the other optimization parameters, the adjusted value of theparameter being the nominal values plus or minus an increment.
 9. Themethod of claim 1 wherein the one or more parameter selection criteriacomprise: a confidence interval threshold of an optimization parameter,the confidence interval threshold being the amount of change from thenominal value of an optimization parameter that results in a change inthe simulated diffraction signal greater than a measured or simulatednoise level for the optimization parameter, the rest of the optimizationparameters being held constant at respective nominal values.
 10. Themethod of claim 1 wherein the one or more parameter selection criteriacomprise: a correlation cutoff, the correlation cutoff being acorrelation coefficient between an optimization parameter and anotheroptimization parameter of the profile model; a sensitivity threshold ofan optimization parameter, the sensitivity threshold being thesum-squared-error of a first simulated diffraction signal calculatedusing nominal values for all the optimization parameters compared to asecond simulated diffraction signal calculated using an adjusted valueof the optimization parameter and nominal values for all the otheroptimization parameters, the adjusted value of the parameter being thenominal values plus or minus an increment; and a confidence intervalthreshold of an optimization parameter, the confidence intervalthreshold being the amount of change from the nominal value of anoptimization parameter that results in a change in the simulateddiffraction signal greater than a measured or simulated noise level forthe optimization parameter, the rest of the optimization parametersbeing held constant at respective nominal values.
 11. The method ofclaim 1 wherein selecting the profile model for use in optical metrologyof the structure in the wafer further comprises: obtaining structurecharacterization; selecting measured diffraction signals for profilemodel and parameter processing; and creating a profile model of thestructure using the structure characterization, wherein the structurehaving a layer stack, the layer stack having one or more layers,structure characterization includes layer stack information about thestructure, each layer stack information comprising material of layer,pitch of repeating structures, line-to-space ratio of repeatingstructures, and optical microscopy data.
 12. The method of claim 11wherein selecting measured diffraction signals for profile model andparameter processing comprises: categorizing input measured diffractionsignals into groups; and selecting a representative measured diffractionsignal from each group of categorized input measured diffractionsignals.
 13. The method of claim 12 wherein categorizing input measureddiffraction signals into groups involves clustering and/or correlationtechniques.
 14. The method of claim 11 wherein creating the profilemodel of the structure using the structure characterization furthercomprises; determining one or more types of geometric shapes for eachmaterial in the layer stack; generating the types of geometric shapesand associated geometric parameters for each geometric shape for alllayers of the layer stack; obtaining nominal values and ranges of thegeometric parameters, the ranges of the geometric parameters being theprobable low and high values of the geometric parameters; definingdependencies of the geometric parameters; and converting the geometricparameters into optimization parameters.
 15. The method of claim 14wherein the geometric shapes comprise rectangles and/or trapezoids. 16.The method of claim 14 wherein defining dependencies of the geometricparameters include: expressing a geometric parameter as a function ofanother geometric parameter, as a function of a variable, as a constant,or as a function of another geometric parameter and/or a variable plusor minus an offset, wherein the offset may be a constant or anothervariable.
 17. The method of claim 14 wherein converting the geometricparameters into optimization parameters comprises: translating thedependencies of the geometric parameters into equations; and performingmathematical operations on the equations that reduce the number ofindependent variables, the independent variables being the optimizationparameters used for the parameter selection process.
 18. The method ofclaim 1 wherein selecting the set of parameters for the profile modelusing one or more input measured diffraction signals and the one or moreparameter selection criteria further comprises: selecting wavelengthsfor optical metrology; calculating values of the one or more parameterselection criteria; selecting optimization parameters that meet the oneor more parameter selection criteria; and performing a procedure todetermine an optimized simulation diffraction signal corresponding to ameasured diffraction signs of the one or more input measured diffractionsignals using the selected optimization parameters of the profile model.19. The method of claim 18 wherein selecting wavelengths for opticalmetrology comprises: selecting wavelengths that meet a noise levelcriteria, the noise level being the standard deviation of diffractionsignals off the same site in a wafer; and selecting wavelengths thathave low correlation of diffraction signals compared to diffractionsignals of other wavelengths.
 20. The method of claim 18 whereinselecting optimization parameters that meet the one or more parameterselection criteria includes: selecting optimization parameters that meeta correlation cutoff, the correlation cutoff being a preset correlationcoefficient value of simulated diffraction signals between anoptimization parameter and another optimization parameter of the profilemodel.
 21. The method of claim 18 wherein selecting optimizationparameters that meet the one or more parameter selection criteriaincludes: selecting optimization parameters that meet a sensitivitythreshold of an optimization parameter, the sensitivity threshold beingthe sum-squared-error of a first simulated diffraction signal calculatedusing nominal values for all the optimization parameters compared to asecond simulated diffraction signal calculated using an adjusted valueof the optimization parameter and nominal values for all the otherOptimization parameters, the adjusted value of the optimizationparameter being the nominal value plus or minus an increment.
 22. Themethod of claim 18 wherein selecting optimization parameters that meetthe one or more parameter selection criteria includes: selectingoptimization parameters that meet a confidence interval threshold, theconfidence interval threshold being the amount of change from thenominal value of an optimization parameter that results in a change inthe simulated diffraction signal greater than a measured or simulatednoise level for the optimization parameter, the rest of the optimizationparameters being held constant at respective nominal values.
 23. Themethod of claim 18 wherein performing the procedure to determine theoptimized simulation diffraction signal corresponding to the measureddiffraction signal using the selected optimization parameters of theprofile model further comprises: utilizing an optimization procedure tofind the simulation diffraction signal that yields the least errorcompared to the measured diffraction signal.
 24. The method of claim 23wherein the optimization procedure utilizes one or more globaloptimization techniques including branch-and-bound technique, simulatedannealing, genetic algorithm, other global optimization technique orhybrid global and local optimization technique.
 25. The method of claim1 further comprising: saving into a data store identification dataassociated with the structure, the wafer, and the selected model anddata about the termination criteria, the one or more parameter selectioncriteria, and the selected optimization parameters.
 26. A method ofdetermining wafer structure having critical dimensions, profile shape,and film thickness using optical metrology, the method comprising: a)setting one or more termination criteria; b) setting one or moreparameter selection criteria; c) selecting a profile mode!for use inoptical metrology of a structure in a wafer, the profile model having aset of geometric parameters associated with dimensions of the structure,the profile model having critical dimensions, profile shape, and filmthickness; d) selecting a set of optimization parameters for the profilemodel using one or more input measured diffraction signals and the oneor more parameter selection criteria, wherein the set of optimizationparameters is converted from the set of geometric parameters, andwherein the number of optimization parameters within the set ofoptimization parameters is less than the number of geometric parameterswithin the set of geometric parameters; e) testing the selected profilemodel and the set of optimization parameters against the one or moretermination criteria; f) performing the steps c, d, and e until the oneor more termination criteria are met; and g) assessing criticaldimensions, profile shape, and film thickness associated with theselected profile model and selected optimization parameters of theselected profile model.
 27. The method of claim 26 further comprising:displaying critical dimensions, profile shape, and film thicknessassociated with the one or more diffraction signal.
 28. A method ofcreating a library of optical metrology signals and associated profilesfor structures in a wafer, the method comprising: a) setting one or moretermination criteria; b) setting one or more parameter selectioncriteria; c) selecting a profile model for use in optical metrology of astructure in a wafer, the profile model having a set of geometricparameters associated with dimensions of the structure, the profilemodel having critical dimensions, profile shape, and film thickness; d)selecting a set of optimization parameters for the profile model usingone or more input measured diffraction signals and the one or moreparameter selection criteria, wherein the set of optimization parametersis converted from the set of geometric parameters, and wherein thenumber of optimization parameters within the set of optimizationparameters is less than the number of geometric parameters within theset of geometric parameters; e) testing the selected profile model andthe set of optimization parameters against the one or more terminationcriteria; f) performing the steps c, d, and e until the one or moretermination criteria are met; g) assessing critical dimensions, profileshape, and film thickness associated with the selected profile model andselected optimization parameters of the selected profile model; and h)creating a library of diffraction signals and associated profile datausing the selected optimization parameters of the selected profilemodel.
 29. A system for processing optical metrology data for waferstructures, the system comprising: a model generator configured togenerate a profile model for a structure in a wafer usingcharacterizations of the structure and to process one or moretermination criteria and one or more parameter selection criteria; anoptical metrology simulator configured to use the profile model andselected optimization parameter values to calculate a simulateddiffraction signal; a parameter selector coupled to the model generatorand to the optical metrology simulator, the parameter selectorconfigured to perform calculations of one or more parameter selectioncriteria values using one or more input measured diffraction signals, tocompare the calculated one or more parameter selection criteria valuesto the one or more parameter selection criteria, and to selectoptimization parameters that meet the one or more parameter selectioncriteria, wherein the optimization parameters are converted from a setof geometric parameters, and wherein the number of optimizationparameters is less than the number of geometric parameters within theset of geometric parameters; and a profile model tester coupled to theparameter selector, the profile model tester configured to performcalculations of termination values, to compare the calculatedtermination values to the one or more termination criteria, and toadjust the profile model if the one or more termination criteria are notmet.
 30. The system of claim 29 further comprising: a profile compilercoupled to the optical metrology simulator, to the model generator, andto the profile model tester, the profile compiler configured to processinput data including characterizations of the wafer structure, waferfabrication process, wafer layer stack, design nominal dimensions ofwafer structure, and expected ranges of dimensions of the waferstructures.
 31. The system of claim 29 further comprising: a data storecoupled to the profile model tester, the data store configured to storeidentification data associated with the structure, the wafer, and theselected model and data about the termination criteria, the one or moreparameter selection criteria, and the selected optimization parameters.32. The system of claim 29 further comprising: a library generatorcoupled to the profile model tester and the optical metrology simulator,the library generator configured to utilize structure profile data fromthe profile model tester and invoke the optical metrology simulator tocalculate simulated diffraction signals.
 33. The system of claim 29further comprising: a library coupled to the library generator, thelibrary configured to contain diffraction signals and associatedstructure profile data.
 34. The system of claim 29 wherein the profilemodel tester further comprises: one or more optimization enginesconfigured to utilize one or more global optimization algorithmsincluding branch-and-bound technique, simulated annealing, geneticalgorithm, other global optimization technique or hybrid global andlocal optimization technique.
 35. The system of claim 29 furthercomprising: a terminal coupled to the profile compiler and to the modelgenerator, the terminal configured to: accept input data includingcharacterizations of the wafer structure, wafer fabrication process,wafer layer stack, design nominal dimensions of wafer structure,expected ranges of dimensions of the wafer structures; and acceptspecification of geometric shapes for profile models and dependencies ofparameters of the geometric shapes.
 36. The system of claim 35 furthercomprising: a critical dimension server coupled to the parameterselector, the critical dimension server configured to display structuredata including critical dimensions, structure profile, and filmthickness corresponding to measured diffraction signals.
 37. The systemof claim 36 wherein the critical dimension server comprises one or moreremote computer devices.
 38. The system of claim 36 wherein the terminaland the critical dimension server reside in a single remote computersystem.
 39. A wafer structure critical dimension server systemcomprising: a metrology model optimizer configured to: a) set one ormore termination criteria; b) set one or more parameter selectioncriteria; c) select a profile model for use in optical metrology of astructure in a wafer, the profile model having a set of geometricparameters associated with dimensions of the structure; d) select a setof optimization parameters for the profile model using one or more inputmeasured diffraction signals and the one or more parameter selectioncriteria, wherein the set of optimization parameters is converted fromthe set of geometric parameters, and wherein the number of optimizationparameters within the set of optimization parameters is less than thenumber of geometric parameters within the set of geometric parameters;e) test the selected profile model and the set of optimizationparameters against the one or more termination criteria; and f) performsteps c, d, and e until the one or more termination criteria are met;and a profiler workstation coupled to the metrology model optimizer, theprofiler workstation configured to: a) receive input regarding waferstructure profiles, the metrology model specifications, the one or moretermination criteria, and the one or more parameter selection criteria;and b) display output information comprising critical dimensions,profile shape, and film thickness of the wafer structures.
 40. Thesystem of claim 39 wherein the profiler workstation comprises one ormore computer systems at remote locations.
 41. The system of claim 39wherein the metrology model optimizer is further configured to: g)create a library of diffraction signals and associated profile datausing the selected optimization parameters of the selected profilemodel.
 42. A system for real-time determination of profile data of waferstructures, the system comprising: an optical metrology systemconfigured to measure diffraction signals off wafer structures; ametrology model optimizer coupled to the optical metrology system, themetrology model optimizer configured to: process characterization ofwafer structure profiles, metrology model specifications, one or moretermination criteria, and one or more parameter selection criteria;generate one or more profile models of the wafer structures, the profilemodels having associated parameters; select a set of optimizationparameters of the profile model using one or more input measureddiffraction signals the selected optimization parameters meeting the oneor more selection criteria, wherein the optimization parameters areconverted from a set of geometric parameters, and wherein the number ofoptimization parameters is less than the number of geometric parameterswithin the set of geometric parameters; and perform the generation ofone or more profile models and selection of optimization parameters ofthe model, the selected optimization parameters meeting the one or moreparameter selection criteria until the one or more termination criteriaare met; a profiler workstation coupled to the metrology modeloptimizer, the profiler workstation configured to: receive inputregarding the wafer structure profiles, the metrology modelspecifications, the one or more termination criteria, and the one ormore parameter selection criteria; and display output informationcomprising critical dimensions, profile shape, and film thickness of thewafer structures; and a data store coupled to the profile model tester,the data store configured to: store identification data associated withthe structure, the wafer, and the selected model and data about thetermination criteria, the one or more parameter selection criteria, andthe selected optimization parameters.
 43. The system of claim 42 furthercomprising: a fabrication cluster coupled to the optical metrologysystem and the metrology model optimizer, the fabrication clusterconfigured to: perform one or more processes in the manufacture ofwafers and wafer structures.
 44. A computer-readable storage mediumcontaining computer executable code to select a profile model for use inintegrated circuit optical metrology, comprising instructions for: a)setting one or more termination criteria; b) setting one or moreparameter selection criteria; c) selecting a profile model for use inoptical metrology of a structure in a wafer, the profile model having aset of geometric parameters associated with dimensions of the structure;d) selecting a set of optimization parameters for the profile modelusing one or more input measured diffraction signals and the one or moreparameter selection criteria, wherein the set of optimization parametersis converted from the set of geometric parameters, and wherein thenumber of optimization parameters within the set of optimizationparameters is less than the number of geometric parameters within theset of geometric parameters; e) testing the selected profile model andthe set of optimization parameters against the one or more terminationcriteria; and f) performing the steps c, d, and e until the one or moretermination criteria arc met.
 45. The computer storage medium of claim44 wherein selecting the profile model for use in optical metrology ofthe structure in the wafer further comprises instructions for: obtainingstructure characterization; and creating a profile model of thestructure using the structure characterization, wherein the structurecharacterization includes layer stack information about the structure,each layer of the layer stack being made of a material, pitch ofrepeating structures, line-to-space ratio of repeating structures, andoptical microscopy data.
 46. The computer storage medium of claim 44wherein creating the profile model of the structure using the structurecharacterization further comprises instructions for: determining one ormore types of geometric shapes for each material in the layer stack;generating the types of geometric shapes and associated geometricparameters for each geometric shape for all layers of the layer stack;obtaining nominal values and ranges of the geometric parameters, theranges of the geometric parameters being the probable low and highvalues of the geometric parameters; defining dependencies of thegeometric parameters; and converting the geometric parameters intooptimization parameters.
 47. The computer storage medium of claim 44wherein selecting the set of parameters for the profile model using oneor more input measured diffraction signals and the one or more parameterselection criteria further comprises instructions for: selectingwavelengths for optical metrology; calculating values of the one or moreparameter selection criteria; selecting optimization parameters thatmeet the one or more parameter selection criteria; and performing aprocedure to determine an optimized simulation diffraction signalcorresponding to a measured diffraction signal of the one or more inputmeasured diffraction signals using the selected optimization parametersof the profile model.
 48. The computer storage medium of claim 47wherein performing procedure to determine an optimized simulationdiffraction signal to a measured diffraction signal using the selectedparameters of the profile model further comprises instructions for:utilizing an optimization procedure to find the simulation diffractionsignal that yields the least error compared to the measured diffractionsignal.
 49. The computer storage medium of claim 44 further comprisinginstructions for: saving into a data store identification dataassociated with the structure, the wafer, and the selected model anddata about the termination criteria, the one or more parameter selectioncriteria, and the selected optimization parameters.
 50. Acomputer-readable storage medium containing computer executable code toselect a profile model for use in integrated circuit optical metrologyby instructing a computer to operate as follows: a) setting one or moretermination criteria; b) setting one or more parameter selectioncriteria; c) selecting a profile model for use in optical metrology of astructure in a wafer, the profile model having a set of geometricparameters associated with dimensions of the structure, the profilemodel having critical dimensions, profile shape, and film thickness; d)selecting a set of optimization parameters for the profile model usingone or more input measured diffraction signals and the one or moreparameter selection criteria, wherein the set of optimization parametersis converted from the set of geometric parameters, and wherein thenumber of optimization parameters within the set of optimizationparameters is less than the number of geometric parameters within theset of geometric parameters; e) testing the selected profile model andthe set of optimization parameters against the one or more terminationcriteria; f) performing the steps c, d, and e until the one or moretermination criteria are met; and g) assessing critical dimensions,profile shape, and film thickness associated with the selected profilemodel and selected optimization parameters or the selected profilemodel.
 51. A computer-readable storage medium containing computerexecutable code to select a profile model for use in integrated circuitoptical metrology by instructing a computer to operate as follows: a)setting one or more termination criteria; b) selling one or moreparameter selection criteria; c) selecting a profile model for use inoptical metrology of a structure in a wafer, the profile model having aset of geometric parameters associated with dimensions of the structure,the profile model having critical dimensions, profile shape, and filmthickness; d) selecting a set of optimization parameters for the profilemodel using one or more input measured diffraction signals and the oneor more parameter selection criteria, wherein the set of optimizationparameters is converted from the set of geometric parameters, andwherein the number of optimization parameters within the set ofoptimization parameters is less than the number of geometric parameterswithin the set of geometric parameters; e) testing the selected profilemodel and the set of optimization parameters against the one or moretermination criteria; f) performing the steps c, d, and e until the oneor more termination criteria are met; g) assessing critical dimensions,profile shape, and film thickness associated with the selected profilemodel and selected optimization parameters of the selected profilemodel; and h) creating a library of diffraction signals and associatedprofile data using the selected optimization parameters of the selectedprofile model.
 52. The computer-readable storage medium of claim 51further comprising stored data including: identification data associatedwith a structure, a wafer, a profile model termination criteria data;one or more parameter selection criteria; and a selected set ofoptimization parameters of a system, for selecting a profile model andselecting parameters of the profile model for use in optical metrologyof structures in a wafer, wherein the selected optimization parametersare selected using one or more input measured diffraction signals andthe one or more parameter selection criteria.